TL;DR - Just skip to the charts for the easy to look at stuff.

Different champions perform differently in different team comps and when vs different team comps.

The perfect example of this is, 2015 MSI finals. Where his holiness Faker lost his first game ever in a competitive game on LeBlanc his trademark champion against EDG, who baited SKT T1 into picking her and drafted the perfect team comp to shut LeBlanc down.

This wasn't helped by the fact that SKT put Bang on a relatively low damage adc, Urgot, hence even more pressure was on Faker to carry.

1) Incredibly tanky frontline with easy to land CC.
2) Sivir who has Spellshield to limit LeBlancs ability to burst her down.
3) Morgama mid who has an extra MR/spellshield just in case.

Faker was still very impactful in that game, far more than most LeBlanc players would be able to be in such a scenario, but the game still went disgustingly in favour of EDG who slowly throttled the game in their favour.

This is because team comp naturally matters.

Some games are a lot more difficult to win when played by a particular champion over another.

A challenger in Bronze playing Sejuani ought to still win 100% of all his games consistently, admittedly he might be going full AP Sejuani. But when going against even high Plats, or low Diamonds - it'd be unsuprising for the Challenger jungler to lose some games just because even though Sejuani is a strong jungler that scales well and has high impact in teamfights with her ultimate, against certain team comps Sejuani will struggle to have the same degree of impact.

An obvious example would be, a team comp where all the carries are mobile, and the enemy team has an early game jungler who manages to snowball due to 'uncontrollable factors..

This could be done to an extreme level of analysis & accuracy, but for those like me who want a simpler model - and it defo seems like many do, I've designed a simple set of charts to help you choose which champion to pick for each role in certain scenarios.

These charts are meant as a simple reference, so you can always change your mind.
Maybe you shouldn't definitely pick them, but they are good scenarios to pick them into.
I have probably also ignored many.

For example,

you might be suprised to find me putting Volibear or Sion as strong in a particular scenario - that is, against a low damage team.

I'll have come to a conclusion based on facts like, how they are both champions that have a strong ability to both take damage and output damage.

http://imgur.com/FgB6Den

Some things will be implicitly implied also. For example, Graves is another champion I recommenced to pick against low damage teams. However, Graves will be less performant against teams with high reliable damage.

http://imgur.com/a/ubPao

These Charts help remind me of when picking more 'fun' champs are definitely viable picks, than just the generic meta OPs.

If any1 creates better ones - be sure to message me, cus I'd be interested in checking them out too.